Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Abstract

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inönü-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planckscale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant. * Electronic address: antonino.marciano@cpt.univ-mrs.fr † Electronic address: r.bruno@bnrenergia.it ‡ Electronic address: gianluca.mandanici@istruzione.it

Kinematics of particles with quantum-de Sitter-inspired symmetries

“…In fact, we study here the kinematics of free particles whose symmetries are compatible with the q-de Sitter Hopf algebra, [22,33,43] which is a quantum deformation of the de Sitter algebra. In particular, as discussed below, we choose the relation between the quantum deformation parameter and the Planck length l and the inverse of the de Sitter radius H such that in the l → 0 limit the algebra contracts to the standard de Sitter algebra, which was discussed in Sec.…”

“…II. The algebra of generators reads, at all orders in the deformation parameter w [33], The coalgebra, which is associated with the action of symmetry transformations over interacting particles and to conservation rules in interactions, is 10 ΔðP 0 Þ ¼ P 0 ⊗ I þ I ⊗ P 0 ;…”

“…1 Despite the fact that most of the research on relativistically compatible deformations of particles' kinematics focuses on cases where spacetime is flat, as mentioned before the best opportunities for phenomenology are found in contexts where spacetime curvature should not be neglected. Only very recently, after early attempts [33][34][35][36] that were however lacking a full understanding of the relative-locality effects produced by momentum space curvature [29][30][31], there have been some proposals to coherently describe nontrivial momentum space properties alongside curvature of spacetime in a relativistic way. Some [37][38][39] have focused on finding an appropriate geometrical description of phase space.…”

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

“…In this framework, spacetime curvature (or nonzero cosmological constant) should play a relevant role concerning 2 Advances in High Energy Physics the possible cosmological consequences of a quantum spacetime (see, e.g., [38,[47][48][49][50][51] and references therein). Therefore, it seems natural to consider the construction of thedeformation for the (anti-)de Sitter (hereafter (A)dS) groups, and to analyse their possible connections with quantum gravity theories with a nonzero cosmological constant.…”

AdS Poisson homogeneous spaces and Drinfel’d doubles

“…However, much less is known about their counterparts for non-vanishing cosmological constant, quantum de Sitter and anti de Sitter space (see [11] and references therein). This is regrettable since they could serve as mathematical models of quantum spacetimes with non-vanishing curvature and with possible cosmological implications, see [12][13][14][15].…”